Churchill and Thomas in 2012 introduced the subdivision of "class 3c late" into: 

• 3d1 - With wedge tailed R and a bust with a pointed face that was largely issued after the closure of the provincial mints – see The Brussels Hoard of 1908 book, p.38-39), and
• 3d2 - With ball-footed R and a bust of improved quality and closely related to that of class 4 coins.

Sub-class 3d2 differs from 3d1 in having a different style of letter R than 3d1 (Ball-shaped foot, R2,  versus a wedge shaped R1) and a broader bust more like that of class 4 coins.   3c coins from non-provincial mints can be distinguished  from 3d1 by the shape of the bust; with busts of sub-class 3d1 being smaller, neater, and with a more pointed chin.  3d2 are relatively easy to identify - their busts being similar to those of class 4, they have the diagnostic ball-footed R, and additionally the inner circle on the reverse tends to be made of smaller pellets, thus allowing a greater number in each quadrant. Prior to the publication of the Churchill and Thomas study, all the above were usually described as 3c, sometimes being sub-divided into 3c early and 3c late.  

Varieties of 3d2 include types with a single pellet after REX and with a colon after REX, as well as varieties with no punctuation marks

In a 2015 article, on the henry3.com website, Ian Heavisides and Robert Page proposed the introduction of class 3d3 for class 3d2 coins having an eight-limbed initial mark, as seen in class 4, rather than the usual six-limbed initial mark.  These coins are only seen from the London mint. This 3d3 group can be further sub-divided into two groups, those bearing a colon in the legend after REX and those where there is a simple single pellet stop. 

Whether sub-class 3d3 was a late issue, so late that the dies did not reach Canterbury or Bury or whether they were produced as a parallel issue to some 3d2 dies is debatable.  Churchill & Thomas recorded 5 coins with mm 5 that were amongst 16 coins displaying a 3d2 obverse paired with a 3d1 reverse, in the Brussels Hoard, suggesting that the issue was early enough to be paired with remaining reverses with the wedge-tailed R1.  

BNS Research Blog Reference    I. Heavisides & R. Page,  2020,   Henry III Long Cross – The Subdivision of Class 3d